Star chain satellite two-line element orbit prediction error compensation method and system based on deep learning

Abstract

The invention discloses a deep learning-based star chain satellite two-line element orbit prediction error compensation method and system. The prediction error compensation method comprises the following steps of: obtaining to-be-predicted star chain satellite two-line element sample data; the sample data are input into an error compensation forecasting model, a forecasting result is obtained, the error compensation forecasting model is constructed through a neural network and obtained through training of a training set, and the training set is star chain satellite two-line element data. The method solves the randomness of error propagation through the excellent mining capability of a deep learning neural network to data features, carries out forecasting according to at least one periodic time interval by batch star chain TLEs, carries out error compensation by using an actual reference orbit result and a propagation orbit result, and dynamically adjusts an operation strategy according to an error analysis result. Therefore, the stability and applicability of the model in different environment states are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of space situation awareness, and particularly relates to a method and system for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning. Background Technique

[0002] With the increasing development of current aviation technology, the number of on-orbit satellites is increasing day by day. With the accumulation of satellite launches, the number of on-orbit satellites is increasing, and the demand for means of orbit prediction is also increasing day by day to obtain more accurate aircraft orbital data. At the same time, with the increase in on-orbit satellites, the growth rate of space debris is also very fast, and the orbital prediction of satellites is very important for maintaining the normal operation of satellites.

[0003] With the continuous increase of space debris and the development of space debris management plans, it is necessary to predict orbits more accurately. Accurately predicting the orbits of low-earth orbit satellites is of great significance for ensuring the safe operation of satellites, optimizing mission scheduling, and improving service quality. However, traditional orbit prediction methods often have great limitations when facing complex space environments, non-linear orbit changes, and uncertain perturbation factors. Therefore, exploring new orbit prediction methods, especially prediction methods based on deep learning, has become a research hotspot.

[0004] Deficiencies of the prior art:

[0005] Currently, the method for predicting the orbit of a satellite is to predict the orbit information of a space target within a certain period of time after that based on a model built according to orbital dynamics on the premise of knowing the state of a space target at a certain moment. Its essence is a process of solving the differential equation describing the motion of the space target; the analytical method is based on Kepler's laws of motion and perturbation theory, and describes the motion law of the satellite through an analytical expression, but this method is difficult to handle complex perturbations and non-linear effects; the numerical method predicts the orbit by solving the satellite motion equation. Although it can consider more influencing factors, the calculation amount is large, and it is highly sensitive to initial conditions and model parameters. Summary of the Invention

[0006] To solve the above technical problems, the present invention proposes a method and system for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning, which can make up for the gap in the problem of error accumulation over time in existing methods and solve the randomness problem of error propagation.

[0007] The present invention provides a method for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning, including:

[0008] Obtaining the two-line element sample data of the Starlink satellite to be predicted;

[0009] Input the sample data into the error compensation prediction model to obtain a prediction result, where the error compensation prediction model is constructed by a neural network and obtained through training with a training set, and the training set is the two-line element data of Starlink satellites.

[0010] Optionally, obtaining the training set includes:

[0011] Obtain the two-line element data of Starlink satellites;

[0012] Perform batch processing and cleaning on the two-line element data of Starlink satellites to obtain the training set.

[0013] Optionally, performing batch processing and cleaning on the two-line element data of Starlink satellites includes:

[0014] Unify the format of the two-line element data of Starlink satellites to obtain uniformly formatted data;

[0015] Sort the uniformly formatted data according to the timestamp, remove the invalid data and missing data after sorting, and extract the orbital parameter features after sorting.

[0016] Optionally, inputting the sample data into the error compensation prediction model to obtain a prediction result includes:

[0017] Based on the sample data, determine the optimal orbit prediction strategy;

[0018] Perform error compensation based on the optimal orbit prediction strategy to obtain a prediction result.

[0019] Optionally, based on the sample data, determining the optimal orbit prediction strategy includes:

[0020] Divide the sample data into orbital data for different time periods;

[0021] Perform coordinate transformation on the orbital data for different time periods to obtain orbital data in the geocentric inertial coordinate system;

[0022] Analyze the orbital data in the geocentric inertial coordinate system to obtain the optimal orbit prediction strategy.

[0023] Optionally, performing coordinate transformation on the orbital data for different time periods to obtain orbital data in the geocentric inertial coordinate system includes:

[0024] Calculate the rotation matrix:

[0025]

[0026] where, θ gmst is the earth's rotation angle;

[0027] The orbital data in the geocentric inertial coordinate system is obtained by multiplying the coordinate vector in the true equator mean equinox coordinate by the rotation matrix:

[0028]

[0029] Among them, is the coordinate vector in the true equator mean equinox coordinate system, is the coordinate vector in the geocentric inertial coordinate system.

[0030] Optionally, analyzing the orbital data in the geocentric inertial coordinate system to obtain the optimal orbit prediction strategy includes:

[0031] Obtaining two-line element data, dividing continuous multiple two-line element data with at least one motion cycle interval into three time periods, and these three time periods respectively correspond to different TLEs: According to the start time of the second time period and the first timestamp of the third time period, intercepting several two-line element data of each time period;

[0032] Using the SGP4 model to calculate the orbital parameters of several two-line element data of each time period to obtain the calculation results;

[0033] According to the calculation results, obtaining the reference orbit;

[0034] Using the reference orbit of the first time period to predict the orbital data of the second time period, comparing the predicted orbit of the second time period with the reference orbit, and calculating the first prediction error;

[0035] Using the predicted orbit of the second time period to predict the orbital data of the third time period, comparing the predicted orbit of the third time period with the reference orbit, and calculating the second prediction error;

[0036] According to the first prediction error and the second prediction error, performing error analysis to obtain the optimal orbit prediction strategy.

[0037] Optionally, training the error compensation prediction model using the training set includes:

[0038] Performing forward propagation based on the input data in the training set to obtain the output data;

[0039] Based on a preset loss function, calculating the loss value between the output data and the target value;

[0040] Calculating the gradients of the parameters in the error compensation prediction model according to the loss value and updating the gradients, that is, performing backpropagation;

[0041] Alternately performing the forward propagation and the backpropagation until the loss function meets the preset conditions and then stopping the training.

[0042] The present invention also provides a two-line element orbit prediction error compensation system for Starlink satellites based on deep learning, comprising: a data acquisition module, an orbit prediction module, an error analysis module, and a compensation module;

[0043] The data acquisition module is used to acquire two-line element sample data of Starlink satellites;

[0044] The orbit prediction module is used to obtain the optimal orbit prediction strategy according to the two-line element sample data of the Starlink satellites;

[0045] The error analysis module is used to perform error analysis based on the optimal orbit prediction strategy;

[0046] The compensation module is used to perform error compensation according to the analysis results.

[0047] Compared with the prior art, the present invention has the following advantages and technical effects:

[0048] The method proposed by the present invention has the ability to process time series in terms of accuracy improvement, effectively captures the long-term dependencies in satellite orbit data, makes up for the gap in the problem of error accumulation over time in existing methods, and solves the randomness problem of error propagation;

[0049] The present invention solves the randomness of error propagation through the excellent ability of the deep learning neural network to mine data features, predicts in batches of Starlink TLEs at least at one-period time intervals, uses the actual reference orbit results and the propagated orbit results for error compensation, and dynamically adjusts the operation strategy according to the error analysis results, and dynamically adjusts the neural network model parameters, data cleaning and preprocessing methods according to the error performance to ensure the stability and applicability of the model in different environmental states. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The drawings forming a part of this application are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0051] Figure 1 is a flowchart of a method for compensating two-line element orbit prediction errors of Starlink satellites based on deep learning according to an embodiment of the present invention;

[0052] Figure 2 is a structural diagram of a two-line element orbit prediction error compensation system for Starlink satellites based on deep learning according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0054] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0055] This embodiment proposes a method for compensating the prediction error of the two-line element orbit of Starlink satellites based on deep learning, as Figure 1 shown, which specifically includes the following steps:

[0056] Obtain the two-line element sample data of the Starlink satellite to be predicted;

[0057] Input the sample data into the error compensation prediction model to obtain the prediction result. Among them, the error compensation prediction model is constructed by a neural network and obtained through training with a training set, and the training set is the two-line element data of the Starlink satellite.

[0058] Specifically, step S1: Use a deep neural network to predict the Starlink orbit samples, analyze the prediction effects under different parameter combinations (such as TLE time interval, etc.) and different linear fitting function fitting orbital arc lengths, and determine the best orbit prediction strategy;

[0059] Step S2: According to the S1 strategy, conduct batch prediction tests on the starlink TLEs, construct a deep neural network model, clean the data of the TLE data set, and construct a reasonable neural network structure according to the characteristics of the data set;

[0060] Step S3: Optimize the parameters of the neural network structure (such as the number of neurons, the number of model layers, etc.) according to the S2 strategy to improve the prediction accuracy of the model;

[0061] Step S4: First, as shown in S1, analyze the sample orbit prediction results under different parameter combinations and linear fitting function fitting orbital arc lengths to determine the best orbit prediction strategy; then, as shown in S3, determine the error compensation prediction model for a large number of tested TLE data; finally, use the prediction result for error compensation to obtain the final prediction result.

[0062] More specifically, if the error continues to increase over time, it indicates that there is drift or error accumulation in the model. In this case, the scale of the training set can be increased, more TLE data for more time periods can be introduced for training, the learning rate and batch size can be modified, and the model parameters can be optimized. If the error remains stable or decreases, it means that the current prediction strategy is stable, and no adjustment is needed. When the error fluctuates periodically, it indicates the presence of periodic perturbations or resonances, and periodic error compensation can be performed on the periodic parameters. The adjustment of the number of neurons can be made according to the data fitting situation. If the number of neurons is too small, it is easy to cause underfitting of the data and ineffective learning of the orbital pattern. If the number is too large, it will cause overfitting of the data, and the performance on new data may be poor when processing TLE data in batches. When the error fluctuates greatly, the model noise has a large impact. The cleaning rules of the data can be enhanced to eliminate abnormal TLE data. Secondly, the prediction duration can be dynamically adjusted, shortening or lengthening the prediction period according to the error situation.

[0063] Further, obtaining the training set includes:

[0064] Obtaining the two-line element data of Starlink satellites;

[0065] Performing batch processing and cleaning on the two-line element data of Starlink satellites to obtain the training set.

[0066] Further, performing batch processing and cleaning on the two-line element data of Starlink satellites includes:

[0067] Unifying the format of the two-line element data of Starlink satellites to obtain uniformly formatted data;

[0068] Sorting the uniformly formatted data according to the timestamp, removing the invalid data and missing data after sorting, and extracting the orbital parameter features after sorting.

[0069] Specifically, step S2 includes:

[0070] Step S21: Dataset analysis and cleaning;

[0071] TLE data contains the orbital information of a series of satellites. Each TLE data entry includes the orbital parameters of the satellite, such as the satellite catalog number, right ascension of the ascending node, declination of the ascending node, orbital period and other parameters. Before training the deep neural network, it is first necessary to perform batch processing and cleaning on the TLE data. First, unify the format of the TLE data, sort the TLE data according to the timestamp, and extract the orbital parameters in the TLE data as independent features, including eccentricity, orbital period, right ascension of the ascending node, etc. Since the TLE data may have gross errors caused by human observations during observation, remove the invalid data and missing data to ensure that the TLE data has no null values or damaged records.

[0072] Step S22: Conducting large-scale tests on the deep neural network model;

[0073] Batch predict all starlink TLEs counted within a certain period, analyze the prediction results and calculate the prediction errors.

[0074] Furthermore, input the sample data into the error compensation prediction model to obtain the prediction results including:

[0075] Based on the sample data, determine the optimal orbit prediction strategy;

[0076] Perform error compensation based on the optimal orbit prediction strategy to obtain the prediction results.

[0077] Furthermore, based on the sample data, determining the optimal orbit prediction strategy includes:

[0078] Divide the sample data into orbit data for different time periods;

[0079] Perform coordinate transformation on the orbit data for different time periods to obtain the orbit data in the Earth-centered Inertial Coordinate System;

[0080] Analyze the orbit data in the Earth-centered Inertial Coordinate System to obtain the optimal orbit prediction strategy.

[0081] Specifically, step S1 includes:

[0082] Step S11: Collect the TLE data of Starlink satellites, and divide the sample data into orbit data for different time periods (such as the first period, the second period, the third period, etc.) according to the time interval;

[0083] Step S12: Convert the Starlink orbit in the True Equator Mean Equinox (TEME) coordinate system to the Earth-centered Inertial Coordinates (ECI); TEME is applicable to TLE data, but in actual applications, the orbit data is generally expressed in ECI. The main difference between the TEME and ECI coordinate systems is that the coordinate axes change with time. The coordinate axes in the TEME coordinate system are based on the position of the Earth's equator and the vernal equinox, while the coordinate axes in the ECI coordinate system are fixed and do not change with the Earth's rotation;

[0084] To convert the TEME coordinate system to the ECI coordinate system, the Earth's rotation angle needs to be calculated, which is usually represented by the Greenwich Mean Sidereal Time (GMST). Obtain the current GMST value. Usually, GMST can be calculated from the current UTC time (Coordinated Universal Time), or obtained through astronomical calculation tools such as the SPICE library. Using the current TEME coordinates (X teme , Y teme , Z teme) and the Greenwich Mean Sidereal Time (GMST) at the calculation moment, which is converted through equations (1) and (2):

[0085] 1) Calculate the rotation matrix:

[0086]

[0087] In the formula, θ gmst is the Earth's rotation angle.

[0088] 2) By multiplying the coordinate vector in the TEME coordinate system by the rotation matrix, the coordinates in the ECI coordinate system are obtained:

[0089]

[0090] Step S13: Analyze the prediction effects under different TLE time intervals and determine the optimal orbit prediction strategy;

[0091] Furthermore, analyzing the orbital data in the geocentric inertial coordinate system to obtain the optimal orbit prediction strategy includes:

[0092] Obtain the two-line orbital element data. Divide the continuous multiple two-line element data with at least one motion period interval into three time periods, and these three time periods respectively correspond to different TLEs: According to the start time of the second time period and the first timestamp of the third time period, intercept several two-line orbital element data of each time period;

[0093] Use the SGP4 model to calculate the orbital parameters for several two-line orbital element data of each time period to obtain the calculation results;

[0094] According to the calculation results, obtain the reference orbit, including: Convert the orbital parameters calculated by the SGP4 model and the semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, mean anomaly in the two-line orbital elements into Keplerian orbital elements to obtain the reference orbit;

[0095] Use the reference orbit of the first time period to predict the orbital data of the second time period, compare the predicted orbit of the second time period with the reference orbit, and calculate the first prediction error;

[0096] Use the predicted orbit of the second time period to predict the orbital data of the third time period, compare the predicted orbit of the third time period with the reference orbit, and calculate the second prediction error;

[0097] Conduct error analysis based on the first prediction error and the second prediction error to obtain the optimal orbit prediction strategy.

[0098] Specifically, in step S13: The data of the TLE at least one period apart is divided into three time periods. According to the start time of the second time period and the first timestamp of the third time period, the relevant data part is intercepted from the data of the first time period. The reference orbit of the first time period is used to predict the orbit data of the second time period by using the designed deep learning neural network model method. The predicted orbit of the second time period is compared with the reference orbit to calculate the prediction error. Then, the orbit of the third time period is predicted from the predicted orbit of the second time period to calculate the prediction error. An error analysis is made on the prediction errors of the predicted orbit of the second time period and the predicted orbit of the third time period, and error compensation is carried out;

[0099] Perform root mean square error (RMSE), mean absolute error (MAE), and standard deviation (STD) statistical analyses on the prediction errors of different parameter combinations, and compare the effects of different strategies on the orbit prediction accuracy, as shown in formulas (3), (4), and (5):

[0100] Calculate the error metrics:

[0101]

[0102] In the formula, O pred,i is the i-th predicted orbit; O true,i is the i-th actual reference orbit; n is the total number of samples.

[0103] The smaller the RMSE and MAE, the smaller the difference between the propagated orbit and the reference actual orbit; STD is used to measure the degree of error fluctuation and can help evaluate the stability of the model. According to the loss functions RMSE, MAE, and STD, determine the orbit prediction strategy, and step S13 can be repeated to determine the best orbit prediction strategy.

[0104] More specifically, according to the first prediction error and the second prediction error, based on the comprehensive evaluation of the error change trend and error characteristics, perform error analysis, and use the strategy with smaller error as the best orbit prediction strategy, including:

[0105] Use common error analysis metrics, including but not limited to: position error, the distance difference between the reference orbit and the predicted orbit; velocity error, the difference between the true velocity and the predicted velocity; orbit parameter error, the deviation of orbit elements such as semi-major axis, eccentricity, and inclination from the reference orbit; average error, the average value of errors in different time periods; maximum error, the maximum deviation value; root mean square error;

[0106] Compare the first prediction error and the second prediction error, conduct an error trend analysis, and check: the change trend of the error over time. If the error gradually accumulates and grows over time, it indicates that the accuracy of the strategy model decreases during long-term predictions. If the error remains stable or decreases, it indicates that the prediction effect is good; the periodic change of the error. If the error shows periodic fluctuations, it may be related to satellite orbit resonance or periodic perturbations, and the periodicity can be detected through Fourier transform or autocorrelation analysis; the convergence or divergence of the error. If the error gradually converges, it indicates that the strategy has good convergence and better stability. If the error diverges, it indicates that there are cumulative biases or drifts in the strategy.

[0107] Furthermore, training the error compensation prediction model using the training set includes:

[0108] Perform forward propagation based on the input data in the training set to obtain output data;

[0109] Based on a preset loss function, calculate the loss value between the output data and the target value;

[0110] Calculate the gradients of the parameters in the error compensation prediction model according to the loss value and update the gradients, that is, perform backpropagation;

[0111] Alternately perform forward propagation and backpropagation until the loss function meets the preset conditions and then stop training.

[0112] Specifically, step S3 includes:

[0113] Step S31: Adjust the number of neurons. Too few neurons may lead to underfitting and inability to effectively learn the patterns of the data; too many neurons may lead to overfitting. The optimal number of neurons can be automatically selected through grid search or random search; the learning rate controls the step size of each gradient update. If the learning rate in the model is too large, it may lead to unstable training processes and poor fitting of the training results. If the learning rate is too small, the training efficiency decreases and convergence may not be achieved. To optimize the learning rate, adaptive learning rate optimizers such as Adam and RMSprop can be used, or learning rate decay can also be used; the batch size needs to balance the training speed and the generalization ability of the accuracy.

[0114] Step S32: Establish an evaluation mechanism;

[0115] The input data in the training set is fed into the model to obtain the output of the model. This process is called forward propagation. Then, based on the set loss function, the difference between the model output and the target value is calculated, that is, the loss between the predicted value and the true value, and the gradients of each parameter are calculated according to this loss. Then, the network parameters are updated through the gradient to minimize the loss as much as possible. This process is called backpropagation. By continuously alternating forward propagation and backpropagation until the loss function converges or meets the preset stopping conditions. To avoid the situation where gross errors have a greater impact and to measure the fitting ability of the model, the mean squared error (MSE) and the coefficient of determination (R 2 ) are introduced as the loss function:

[0116]

[0117] In the formula, O pred,i is the i-th predicted orbit; O true,i is the i-th actual reference orbit; n is the total number of sample data participating in the propagation; is the mean of the actual reference orbits.

[0118] R 2 is an index to measure the fitting degree of the model, indicating the correlation between the predicted value and the actual value of the model. The value of R 2 ranges between 0 and 1. The closer it is to 1, the better the model fits. It is standardized, so it is convenient for comparison between different linear fitting functions; MSE is highly sensitive to large errors and can play a role when the goal is to reduce large errors. It has a strong penalty for large errors, so it may make the model performance look poor, but it can avoid the situation where gross errors have a greater impact and measure the fitting ability of the model. According to R 2 and MSE to measure the hyperparameter performance, step S31 can be repeated to determine the optimal parameter configuration.

[0119] Step S4 includes:

[0120] Step S41: Analyze the best prediction strategy for Starlink orbit samples under different parameter combinations and different linear fitting function fitting orbit arc lengths;

[0121] Step S42: Clean the data of the TLE dataset and conduct batch prediction tests on all starlink TLEs;

[0122] Step S43: Optimize the parameters of the neural network structure;

[0123] According to the results of S42, optimize the parameters of the neural network, adjust the number of neurons, control the learning rate, establish an evaluation mechanism, and introduce the mean squared error (MSE) and the coefficient of determination (R 2 ) as the loss function;

[0124] Step S44: Perform error compensation using the prediction result to obtain the final prediction result.

[0125] Specifically, the error compensation strategy is as follows: By continuously updating the training data, using a deep learning neural network to learn the error pattern, combining the deep learning predicted orbit with the SGP4 model to calculate the orbit, compensating for the error, avoiding the accumulation of errors in a single model, and improving the long-term orbit prediction accuracy.

[0126] For non-linear orbit parameters with stable predictions and vulnerable to perturbation effects, use a deep learning neural network for error compensation, learning the temporal characteristics of the error, such as the orbit inclination, eccentricity, and air drag term. Use a deep learning neural network model to learn the orbit evolution error pattern, taking the historical orbit data error as the model input to correct the future orbit prediction error and compensate for the long-term prediction error.

[0127] For orbit parameters with periodic changes, such as the right ascension of the ascending node, argument of perigee, and mean anomaly, due to the periodic change of the orbit angle, such as the mean anomaly cycling between 0° and 360°, when using a deep learning neural network model to predict this type of periodic parameter, the error is relatively large. A linear fitting function can be used for error compensation. The periodic data is spliced and processed, the data of 0° and 360° are merged, and then the spliced data is fitted with a linear fitting function for angle parameter correction and compensation.

[0128] The linear fitting function can adopt the polynomial fitting regression formula:

[0129] f(x) = c0 + c1x + c2x 2 + … + c n x n

[0130] where n is the polynomial order, c i is the regression coefficient, and x is the input angle parameter.

[0131] Finally, fuse the predicted orbit compensated by the deep neural network model with the corrected angle parameter of the linear fitting function to generate the final predicted orbit.

[0132] This embodiment also provides a deep learning-based two-line element orbit prediction error compensation system for Starlink satellites, including: a data acquisition module, an orbit prediction module, an error analysis module, and a compensation module;

[0133] The data acquisition module is used to collect two-line element sample data of Starlink satellites;

[0134] The orbit prediction module is used to obtain the optimal orbit prediction strategy according to the two-line element sample data of Starlink satellites;

[0135] An error analysis module for performing error analysis based on the optimal orbit prediction strategy;

[0136] A compensation module for performing error compensation according to the analysis results.

[0137] Specifically, as Figure 2 shown, the system in this embodiment includes: A data processing module: Collect Starlink TLE data, unify the TLE data format, sort the TLE data according to the time stamp, and extract the orbit parameters in the TLE data as independent features (such as the first period, the second period, the third period, etc.), including eccentricity, orbital period, right ascension of the ascending node, etc.; Since the TLE data may have gross errors caused by artificial observations during observation, remove invalid data and missing data to ensure that the TLE data has no null values or damaged records, and perform TEME→ECI coordinate transformation;

[0138] An orbit prediction module: Train a neural network model, analyze the TLEs dataset, and design a reasonable neural network structure; Perform orbit propagation to generate orbit prediction data;

[0139] An error analysis and compensation module: Perform root mean square error (RMSE), mean absolute error (MAE), and standard deviation (STD) statistical analysis on the prediction errors of different parameter combinations, compare the influence of different strategies on the orbit prediction accuracy, introduce mean square error (MSE) and coefficient of determination (R 2 ) as a loss function to evaluate the model performance; Perform error compensation to adjust the model prediction strategy;

[0140] An optimization and decision-making module: Adjust the number of neurons, and the optimal number of neurons can be automatically selected through grid search or random search; To optimize the learning rate, an adaptive learning rate optimizer such as Adam or RMSprop can be used, or learning rate decay can also be used. The batch size needs to balance the training speed and the accuracy generalization ability; Determine the optimal parameter configuration to improve the propagation accuracy;

[0141] An output module: Use the prediction results to perform error compensation to obtain the final prediction results. This embodiment relates to the field of space situation awareness and is applicable to space monitoring or Starlink management applications.

[0142] The above is only a preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning, characterized in that, Including: Obtain the two-line element set sample data of the Starlink satellites to be predicted; Input the sample data into the error compensation prediction model to obtain the prediction result, where the error compensation prediction model is constructed by a neural network and obtained through training with a training set, and the training set is the two-line element set data of the Starlink satellites.

2. The method for compensating the two-line element orbit prediction error of Starlink satellites based on deep learning according to claim 1, characterized in that Obtaining the training set includes: Obtain the two-line element set data of the Starlink satellites; Perform batch processing and cleaning on the two-line element set data of the Starlink satellites to obtain the training set.

3. A method for compensating the orbital prediction error of the two-line elements of Starlink satellites based on deep learning according to claim 2, characterized in that, Performing batch processing and cleaning on the two-line element set data of the Starlink satellites includes: Unify the format of the two-line element set data of the Starlink satellites to obtain uniformly formatted data; Sort the uniformly formatted data according to the timestamp, remove the invalid data and missing data after sorting, and extract the orbital parameter features after sorting.

4. A method for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning according to claim 1, characterized in that, Inputting the sample data into the error compensation prediction model to obtain the prediction result includes: Based on the sample data, determine the optimal orbit prediction strategy; Perform error compensation based on the optimal orbit prediction strategy to obtain the prediction result.

5. A method for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning according to claim 4, characterized in that, Based on the sample data, determining the optimal orbit prediction strategy includes: Divide the sample data into orbital data for different time periods; Perform coordinate transformation on the orbital data for different time periods to obtain the orbital data in the geocentric inertial coordinate system; Analyze the orbital data in the geocentric inertial coordinate system to obtain the optimal orbit prediction strategy.

6. A method for compensating the orbital prediction error of the two-line elements of Starlink satellites based on deep learning according to claim 5, characterized in that, Performing coordinate transformation on the orbital data for different time periods to obtain the orbital data in the geocentric inertial coordinate system includes: Calculate the rotation matrix: where θ gmst is the angular velocity of the Earth's rotation; By multiplying the coordinate vector in the true equator mean equinox coordinate by the rotation matrix, obtain the orbital data in the geocentric inertial coordinate system: Among them, is the coordinate vector in the true equator mean equinox coordinate system, is the coordinate vector in the geocentric inertial coordinate system.

7. A method for compensating the prediction error of the two-line element orbit of Starlink satellites based on deep learning according to claim 5, characterized in that Analyzing the orbital data in the geocentric inertial coordinate system to obtain the optimal orbit prediction strategy includes: For the obtained two-line orbital element data, divide the continuous multiple two-line element data with at least one orbital period interval into three time periods, and these three time periods correspond to different two-line element sets respectively; According to the start time of the second period and the first timestamp of the third period, intercept several two-line orbital element data for each period; Use the SGP4 model to calculate the orbital parameters for several two-line orbital element data in each period to obtain the calculation result; According to the calculation result, obtain the reference orbit; use the reference orbit in the first period to predict the orbital data in the second period, compare the predicted orbit in the second period with the reference orbit, and calculate the first prediction error; Use the predicted orbit in the second period to predict the orbital data in the third period, compare the predicted orbit in the third period with the reference orbit, and calculate the second prediction error; According to the first prediction error and the second prediction error, based on the comprehensive evaluation of the error change trend and error characteristics, perform error analysis, and use the strategy with smaller error as the optimal orbit prediction strategy.

8. A method for compensating the orbital prediction error of two-line elements of Starlink satellites based on deep learning according to claim 1, wherein, Training the error compensation prediction model with the training set includes: Perform forward propagation based on the input data in the training set to obtain the output data; Based on a preset loss function, calculate the loss value between the output data and the target value; Calculate the gradients of the parameters in the error compensation prediction model according to the loss value and update the gradients, that is, perform backpropagation; Alternately perform the forward propagation and the backward propagation until the loss function satisfies a preset condition and then stop the training.

9. A two-line element orbit prediction error compensation system for Starlink satellites based on deep learning, characterized in that, It includes: a data acquisition module, an orbit prediction module, an error analysis module, and a compensation module; The data acquisition module is used to acquire the two-line element sample data of the Starlink satellites; The orbit prediction module is used to obtain the optimal orbit prediction strategy according to the two-line element sample data of the Starlink satellites; The error analysis module is used to perform error analysis based on the optimal orbit prediction strategy; The compensation module is used to perform error compensation according to the analysis result.

Images